\newproblem{lay:6_7_18}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 6.7.18}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Show that $\|\mathbf{u}+\mathbf{v}\|^2+\|\mathbf{u}-\mathbf{v}\|^2=2\|\mathbf{u}\|^2+2\|\mathbf{v}\|^2$.
}{
   % Solution
	\begin{center}
		$\begin{array}{rcl}
			\|\mathbf{u}+\mathbf{v}\|^2+\|\mathbf{u}-\mathbf{v}\|^2&=&(\mathbf{u}+\mathbf{v})\cdot(\mathbf{u}+\mathbf{v})+
			   (\mathbf{u}-\mathbf{v})\cdot(\mathbf{u}-\mathbf{v})  \\
			 &=&\left(\|\mathbf{u}\|^2+\|\mathbf{v}\|^2+2\mathbf{u}\cdot\mathbf{v}\right)+
			    \left(\|\mathbf{u}\|^2+\|\mathbf{v}\|^2-2\mathbf{u}\cdot\mathbf{v}\right)  \\
			 &=&2\|\mathbf{u}\|^2+2\|\mathbf{v}\|^2  \\
		\end{array}$
	\end{center}
}
\useproblem{lay:6_7_18}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}

